{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Programming Exercise 2: Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1 Logistic Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "datafile = 'data/ex2data1.txt'\n",
    "#!head $datafile\n",
    "cols = np.loadtxt(datafile,delimiter=',',usecols=(0,1,2),unpack=True) #Read in comma separated data\n",
    "##Form the usual \"X\" matrix and \"y\" vector\n",
    "X = np.transpose(np.array(cols[:-1]))\n",
    "y = np.transpose(np.array(cols[-1:]))\n",
    "m = y.size # number of training examples\n",
    "##Insert the usual column of 1's into the \"X\" matrix\n",
    "X = np.insert(X,0,1,axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1 Visualizing the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Divide the sample into two: ones with positive classification, one with null classification\n",
    "pos = np.array([X[i] for i in xrange(X.shape[0]) if y[i] == 1])\n",
    "neg = np.array([X[i] for i in xrange(X.shape[0]) if y[i] == 0])\n",
    "#Check to make sure I included all entries\n",
    "#print \"Included everything? \",(len(pos)+len(neg) == X.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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9HJVTdsEkJb9aPc6k5Fcryi9c5RRsHwVuAN5sZs8CHwf+ryB3WuiLGzCznxX+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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112f99490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plotData():\n",
    "    plt.figure(figsize=(10,6))\n",
    "    plt.plot(pos[:,1],pos[:,2],'k+',label='Admitted')\n",
    "    plt.plot(neg[:,1],neg[:,2],'yo',label='Not admitted')\n",
    "    plt.xlabel('Exam 1 score')\n",
    "    plt.ylabel('Exam 2 score')\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "    \n",
    "plotData()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2 Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from scipy.special import expit #Vectorized sigmoid function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZppRRIXsBi3KmFwOHNLP8+cBD5QQh0pK//x1uvBEmTowdiUg2pDrkr5kdCZwD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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113985710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Quick check that expit is what I think it is\n",
    "myx = np.arange(-10,10,.1)\n",
    "plt.plot(myx,expit(myx))\n",
    "plt.title(\"Woohoo this looks like a sigmoid function to me.\")\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Hypothesis function and cost function for logistic regression\n",
    "def h(mytheta,myX): #Logistic hypothesis function\n",
    "    return expit(np.dot(myX,mytheta))\n",
    "\n",
    "#Cost function, default lambda (regularization) 0\n",
    "def computeCost(mytheta,myX,myy,mylambda = 0.): \n",
    "    \"\"\"\n",
    "    theta_start is an n- dimensional vector of initial theta guess\n",
    "    X is matrix with n- columns and m- rows\n",
    "    y is a matrix with m- rows and 1 column\n",
    "    Note this includes regularization, if you set mylambda to nonzero\n",
    "    For the first part of the homework, the default 0. is used for mylambda\n",
    "    \"\"\"\n",
    "    #note to self: *.shape is (rows, columns)\n",
    "    term1 = np.dot(-np.array(myy).T,np.log(h(mytheta,myX)))\n",
    "    term2 = np.dot((1-np.array(myy)).T,np.log(1-h(mytheta,myX)))\n",
    "    regterm = (mylambda/2) * np.sum(np.dot(mytheta[1:].T,mytheta[1:])) #Skip theta0\n",
    "    return float( (1./m) * ( np.sum(term1 - term2) + regterm ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6931471805599453"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Check that with theta as zeros, cost returns about 0.693:\n",
    "initial_theta = np.zeros((X.shape[1],1))\n",
    "computeCost(initial_theta,X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#An alternative to OCTAVE's 'fminunc' we'll use some scipy.optimize function, \"fmin\"\n",
    "#Note \"fmin\" does not need to be told explicitly the derivative terms\n",
    "#It only needs the cost function, and it minimizes with the \"downhill simplex algorithm.\"\n",
    "#http://docs.scipy.org/doc/scipy-0.16.0/reference/generated/scipy.optimize.fmin.html\n",
    "from scipy import optimize\n",
    "\n",
    "def optimizeTheta(mytheta,myX,myy,mylambda=0.):\n",
    "    result = optimize.fmin(computeCost, x0=mytheta, args=(myX, myy, mylambda), maxiter=400, full_output=True)\n",
    "    return result[0], result[1]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 0.203498\n",
      "         Iterations: 157\n",
      "         Function evaluations: 287\n"
     ]
    }
   ],
   "source": [
    "theta, mincost = optimizeTheta(initial_theta,X,y)\n",
    "#That's pretty cool. Black boxes ftw"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.20349770159\n"
     ]
    }
   ],
   "source": [
    "#\"Call your costFunction function using the optimal parameters of θ. \n",
    "#You should see that the cost is about 0.203.\"\n",
    "print computeCost(theta,X,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x113a80390>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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7ezwe2bBhg4iI/Pjjj3L99dfLscceK8cff7w88MAD/t/Ly8uTvn37Vom/8n1r\ne24tWrSQli1bSs+ePeWFF17w//xI5xIRufXWW6V169aSlJQkzzzzTJUxbJWfW02xLViwQI4//nhp\n27atTJs2Tbp27eofw7Z06VI55ZRTpEWLFtKvXz/Jysqqct/antM//vEP8Xg88uGHH9b4fEVCO4bN\n8eIroKBd/gcYSgcOiDzxhEiHDiLXXitSy9/JEUXSi74baf4CpwVbVVqwhV4sv1+o4CooKJAuXboc\n8XdCWbDppIMIc9RRcMst1rptjz5q7aBw7bXWfqW1jPk8jHZJ2KP5C1xF7mI5h9X3u61Qn/1u3Za3\n6pNH7Dw3pdzs4MGDzJw5k5tuusmxGHQv0Qj33XcwdSo8+6y1ptudd0KLFk5HpZSqj0jf7/ZI8bvl\nucXyXqIqOL766ivOOOMMUlNTyc/P55hjjqn1d3UvUVWrdu1g1iz47DNYvx6Sk61JCr/8Uvt9onmg\nczho/gKnubNH86dU+J1yyins3buXgoKCIxZroaZdolHihBOsVraVK2HCBGuT+QcegGHDrK2wlFLu\nE4ndhPXt9ozE56aUm2mXaJRasgTGjYNDh2D6dGu/UqWUCia3dHseiXaJqnDSLlHVYAMGwKefwr33\nwq23wm9/CytWOB2VUkoppQKhBVsUMwauuAK++AKuvBIuvRSuvhqee87rdGgRTccRBU5zZ4/b8qfd\nnkqFj45hiwFNmsDo0XD99dYEhZtvho8+svYrrbQVm1JKNUgkFGxdunQ5bJshpUKlS5cuIXtsHcMW\ng7Zvh2nTIC/PWtPt7ruhZUuno1JKKaWik45hUwFp0wZmzIDPP4evv4akJKvl7cABpyNTSimlVE20\nYItBFeNgunSxWtnef9/aZP6UU6ylQXw+R8NzPbeNI4okmjt7NH/2aP7s0fw5Sws2Rc+e8OabMH++\nteju6adDfj5or7NSSinlDjqGTVUhAosWWYvvduhgreHWu7fTUSmllFKRS8ewqaAzBoYOheJiuO46\nuPxya2mQdeucjkwppZSKXVqwxaD6jENo3Bj+7/+gpATOPBPS062lQbZuDX18bqfjOAKnubNH82eP\n5s8ezZ+ztGBTRxQXZ21xtW4dtGpljXebOBF27XI6MqWUUip26Bg21SCbN0N2NrzxhlXI3XILHH20\n01EppZRS7qVj2FTYde4Mc+aA1wsFBXDyydbs0rIypyNTqv60a0cpFWm0YItBwXiz6t4dFi6E55+H\nZ56BlBTvtM2VAAAgAElEQVRraZBYaPjUN/vAuSV3bomjoSI1brfQ/Nmj+XOWYwWbMWaCMeZLY8xq\nY8xzxpijjDHxxph3jTHrjDH/Msa0cio+VT/nngtLl1pbXY0fD/36WfuUKqWUUip4HBnDZozpAiwB\nThGRX4wxLwFvA92B7SLysDFmHBAvIuNruL+OYXOhsjL4xz9g8mRIS7OKuG7dnI5KKYvX6/W3EOTk\n5JCVlQVYG5hHwibmSqnIFYwxbE4VbPHAx8A5wB7gNeAvwBPAeSKyzRjTAfCKyCk13F8LNhf7+Wdr\nx4Tp0+HSS61JCscd53RUSv0qOzub7Oxsp8NQSsWIiJ10ICI/AjOAr4EtwC4ReR9oLyLbyn/nW6Cd\nE/FFu1CPQzj6aLjrLmsNt3btoFcva0bpjz+G9LRho+M4Aqe5s0fzZ4/mzx7Nn7McKdiMMScAdwBd\ngN8AzY0x1wHVm820GS2CtW5tdYsWF8POnZCcDA8/DPv3Ox2ZinXaBaqUijROdYkOAy4UkZvKj4cD\nZwPnA/0rdYkuEZHDRkEZY2TkyJEkJiYC0Lp1a1JSUvwvwhWfAvTYXccdOvRn4kRYutRLRgY8+GB/\nGjd2T3x6rMd6rMd6rMfBOK74vrS0FID58+dH7Bi2XsCzwJnAAWAe8BlwPLBDRKbrpAN38vl8FBUV\nAZCamorH42nwY3zyiTWj9LvvrBa4yy6z9jBVSimlolEkj2FbBSwACoFVgAH+DkwHLjTGrAMuAB5y\nIr5oV/kTQEMUFxeRkZFGfn4/8vP7kZGRRnFxUYMf5+yzYckSmDHDmlF67rnWIryRItD8Kc2dXZo/\nezR/9mj+nOVIwQYgIrkicqqInCYiI0XkoIjsEJHfisjJInKRiOx0Kj5Vlc/nIzd3FBkZK0lP30d6\n+j4yMlaSmzsKn8/X4MczBgYNgqIi+POfYfhwuOQS+OKLEASvlNI3W6UinGMFW7Tw+XwUFhZSWFgY\nUOHihIq+9oYoKioiObmEyj2gHg8kJZX4u0gD0aiRVaytWwcXXGB9ZWTA118H/JAhF0j+lEVzZ4+d\n/GnBptefXZo/Z2nBZkOwuggVNG0KY8daS4F07gypqXD33bB9u9ORqWijhYtSKhJpwRagYHcRhlMg\nb1ipqamUlCRT+an5fLB+fTKpqalBi61VK5gyBb78Evbtg1NOsSYm/PRT0E5hm77hB84NuXNDDIFq\naOxer9e/SHBOTo7/+0jOgR2x+ryDRfPnrMZOBxCp6uoiTEtLcy64EPB4PGRmziU3dxRJSSUArF+f\nRGbm3IBmitalQwd48km44w6YNMlawy0rC0aNgsZ61SpVL/3796/SjaW7OygVufStLwYFOg6hZ89U\n8vIKbS/r0RBJSfDSS7BihbVbwowZVovb5Zc7txSIjuMInFO583q9/taBnJycKvFE0v9nJMXqRpo/\nezR/znJkHTa73LAOm8/nIyMjjYyMlf5WNp8P8vJSyMsrDHkhE4tE4L33rDXcmjSx9irV1w/VULG6\nj6jX69U3XBXRIvkajth12KJBRRdhXl4KBQVxFBTEkZfXK2RdhMEUqeMQjIGLLrJa28aOtbpHBw+G\nVavCG0ek5s8NNHf22MlfpL7RBZNef/Y4nT+nz+80d1cWLlfRRTh48FIGD15KXt7n9OwZvAH4qmYe\nD1xzDXz1lVWw/e531tIg5TuAKHVEWrgou2K9cFDO0C7RKBaMbaQiwZ498Oij8PjjcP31MHEiHHus\n01EppaJVrHarO6H6+NOsrCwg8safBqNLVCcdRKni4iJyc0eRnGzN6Jw1K5nMzLlR2QLYooU1g/TP\nf4YHHoBu3eD2260Zpscc43R0SimlAqUznX8VnU0uMa6uNeKitTm/XTv4y1/g009h7VprKZAnn4SD\nB4N7nsr5i9ZcBqI+udB82aP5s8dO/nRNO73+nKYtbFEoVNtIRYoTT4Tnn7f2KR0/Hh57zGp5u/JK\nCHavcCTPWgo2zYWKZtrS47xYf33RFrYAROL+oZXFykWfmgr/+hf87W/wyCPQuzd88IH9x42V/IWC\n5s4ezd+R1dUCpPmzx+n8OX1+p2kLWwNFwtiw1NRUZs1Kpk+fqmvEBXsbqUhxwQWwfDm8+ir86U/Q\ntSs89BCcfnpgjxcti7AGg+ZCuUm4Wnn12lZO0IKtASqPDasohPr0scaGuWmx3Lq2kYrFritjrC7R\noUPhmWdgyBA47zyrq/TEExv+eJW7Q2K5a6Sh3USxeO0Fk+bPnmDlL1b/D/T6c5YWbA0QSfuHOrGN\nVCRo0sSaTTp8OMycCWedZa3pNmkStG/vdHRKqYbSVl4VK3QdtgYoLCwkP78f6en7qtxeUBDH4MFL\nXVWwqfr54QeYOhUWLIBbb4W777aWCakv/cT5K82Fcpquj6bcSremCrPU1FRKSpKpPM8glseGRYO2\nba1ZpIWF8N//WpvNP/44/PJL/e6vBcqvNBfKzXRJChXptGBrgEjeP7QyfeE6XGKi1cr27rvwzjtw\nyinW0iA1TQLW/AVOc2eP5u/IjvShoXLXqQqM5s9ZOoatgXRsWHQ77TR46y348EMYNw5yc60ZpRdd\nZE1cUEq5l7byqmimY9iUqoUI/POfMGECHHecVbideabTUSml6ita9qFUkS8YY9i0YAuTWNmIPRod\nOgTz5kF2Npx7rrUUSHKy01EppRpCJyQoJ+mkgwhRXFxERkYa+fn9yM/vR0ZGGsXFzm0RpeMQGqZx\nY7jpJli/3lps98wzvfz5z/DNN05HFnmqX3t6LTaM5ssezZ89mj9nacEWYnVtxK4iR1yctTfpggVw\nzDHQo4e1ftuuXU5HFrmO9Aagbw4qmLQLVEU6LdhCzI0bsesLlz2XXdaf3Fxrc/mtW63u0ccegwMH\nnI7M/Rpy7WnBdjj92w2cjluzT/PnLJ0lqlSAjj8e5s6FL76Ae++FWbPg/vvhuuugUSOno3MvXZle\nKRVLgvXhUwu2EHPjRuy6Ir091fPXowe8/josW2YtBfLII9aM0kGDdCmQ6ipyV9v+o1rMHZn+7dqj\n+bNH8xcYLdgiRF0bsavokZ5uFW1vvAGZmTB9uvV19tlORxY5GrqZvFJKxQpd1iNMdFmP2HLokDU5\nISvLWrtt2jRr9wRV1ZE+sesyDEqpSFVTb4Guw6YaTIvH8Nm/H554wtoxYehQq4Dr1MnpqCKDdr8o\npaJBdnY2OTk5ug6bapji4iIGDkx2zZpwkagh4xGaNbO6R9etg4QEa+ur8ePhxx9DF5+bNSR3Wqwd\nTmfO2qP5s0fz5ywt2GJIxZpwAwdu0DXhwiw+3pqIsGoVbN8OJ59sTU74+WenI1NKKRVKwfrwqV2i\nMaSwsJD8/H6kp++rcntBQRyDBy8lLS3Nochiz9q1MHEirFgBOTkwYoQuBaKUUtEqYremMsYkG2OK\njDGfl/+7yxhzmzEm3hjzrjFmnTHmX8aYVk7Ep1SodesGr70GL71k7VN62mnW0iD6OUQp7XpTqiaO\nFGwiUiIiqSJyOpAG/AT8ExgPvC8iJwOLgQlOxBetUlNTKSlJ5vPPf73N6TXhIlEw30zOOQc+/BAe\nftja5qpvX/j3v4P28K6jb8T2xEr+QvU8YyV/oaL5c5YbxrD9FtggIpuBy4D55bfPB4Y6FlUUqlgT\n7p13TqSgII6Cgjjy8nrpmnAOMwYuvtja6uqPf7R2SrjsMvjyS6cjczd983CO5j766P+p+7lh4dyr\ngOfLv28vItsARORbY0w758KKTj17pvLOOyW6rIcNoZq92KiRNZZt2DB46ikYMACGDLHGuHXuHJJT\nhl0wcxeLy3645fmGIvfh2OXCLflzo/r8n2r+nOVowWaMaQJcCowrv6n6CB4d0RMCHo9HJxg4qK4X\nxqOPhjvugFGjrPXbUlKs7ydMsJYGUSoa6S4XSh2Z0y1sg4BCEfmh/HibMaa9iGwzxnQAvqvtjhkZ\nGSQmJgLQunVrUlJS/H/sFZ/S9Ljm45kzZ2q+bBzbzV9eXl69f/+BByA11cv8+XDyyf256y5ISfFy\n9NHuyUdDjit3uwR6/4r8zZ9vjZ4oLS0lJSWFsWPHOv78Qn1sN392jiu+Ly0t9eceQvP6W1paWuWc\nwXo+TubPjccN/XvS/AX29xI0IuLYF/ACMLLS8XRgXPn344CHarmfqMAtWbLE6RAimt38ZWVlBXS/\ndetErrhCpFMnkb//XeTgQVthOCKY116geYxkbvnbDXXua3qewXjubsmfG9Xn/zQW8xes51xet9iq\nmRxrYTPGxGFNOPhjpZunAy8bY0YBm4BhTsQW7So+CajABJI/r9fr/+QV6Pic5GR45RVYvtzaLWHG\nDHjwQWvLK2NrdZ/w0WvPnljJX03P0+v12n7+sZK/UInF/AVy3QXjWq2JYwWbiOwDjq122w6sIk6p\nqFK9MLMzPqd3b/jgA3j3XRg3zloS5KGH4Lzz7McZSWLxzcMtNPfRR/9PgyfqCjblnFBdTLHCDfkz\nBn73O7jwQnjhBbjhBmsx3gcftBbhdatg5s7p/wMnuOHag/DlPhgt09Ufzw35c6P65CVW8hfs6y5Y\ntGBTKsyC+Qfv8Vjrtl1xBcyeDRddZH3dfz+Uz8lRKmIFs2VaqfoK5LoLR5Gne4kqFUV277bGtj3x\nhLWm28SJ0Lat01EpZV92drYWbCrsArnuarpPxO4lqpQKjZYtrYV216yBgwfhlFNg6lT46SenI1PK\nnljoilPu46brTgu2GFR5nRjVcJGQv/btrVa2Tz6BL76ApCT429+sIs5JkZA7N4vl/AXjjTOW8xcM\nsZi/QK67UBV5dRZsxphkY8wHxpgvyo9PM8ZMCkk0SqmgOukka1LCG2/Aa6/BqadaS4PoiAKllAqN\nUBVsdY5hM8Z8CGQCs0Uktfy2L0SkR0giqgcdwxY9fD6f7msaRu+/b63h5vFYS4Gcf77TESmlVPQL\n1xi2OBFZXu22Q3ZOqhRAcXERGRlp5Of3Iz+/HxkZaRQXFzkdVlT77W+thXfvugv++EcYOBCKNOUh\nEYvdR0qp0KlPwfaDMeZEyjdiN8ZcAXwT0qhUSLnhjcTn85GbO4qMjJWkp+8jPX0fGRkryc0dhc/n\nczq8I3JD/uzweOCqq6yJCZdeCoMHW0uDbNwY+nNHeu4aIhTPNZbyFwqaP3s0f86qT8F2CzAbOMUY\nswUYC/wppFGpqFdUVERycgmVe0A9HkhKKvF3karQOuoouPlmWL/emk3auzfcdht8953TkSmllKru\niGPYjDEe4AoRedkY0xzwiMiesEVXe1w6hi3CFRYWkp/fj/T0fVVuLyiIY/DgpaSlpTkUWez6/ntr\nCZBnn4UxY+DOO6FFC6ejiizVF8/MysoCnF8hXalAxcruBqEWjDFsR9zpQER8xph7gJdFRFdyUkGT\nmprKrFnJ9Omz0t/K5vPB+vXJpKamOhtcjDr2WJg5E26/He67z9psfuJEa6zbUUc5HV1k0JX5VbRx\na8Hm1rhCqT5dou8bY+42xnQ2xiRUfIU8MlVvPp+PwsJCCgsL6zX+yw3jEDweD5mZc8nLS6GgII6C\ngjjy8nqRmTnX9TNF3ZC/UOra1Wply8+Ht96y9ih94QWroLYr2nMXapo/ezR/9rgpf26KJVzqs5fo\nVeX/3lLpNgFOCH44qqGKi4vIzR1FcnIJALNmJZOZOZeePd3fStWzZyp5eYW6rIdLpaRYRduSJTBu\nHOTmwvTp1obzqm6x9ulfRY/a9sVs3bq1XtcO0r1EI5jP5yMjI42MjKrdinl5KeTlFWrxE+OC2WUg\nAv/v/1ldpJ07W2u4nXFGUB5aKeVibtrDNZLHiIZ8DFv5SZoAfwb6ld/kxVpE1+FNblRdMy114H5s\nC2bBZgxccQVcdhnMm2f9m54ODzxgbXullFKhFutjROvTBPMUkAY8Wf6VVn6bilCx2PcfTLGcvyZN\nrEkIJSXQqxecc461NMi339bv/rGcu2DQ/Nmj+Wu4ygWS5s9Z9RnDdqaI9Kp0vNgYsypUAan605mW\nqrraxp4Eu8ugeXO4914YPRqmTbP2KL3lFrj7bmjZMminUUo5zK1djW6NK5Tqs5fo58CVIrKh/PgE\n4FUROT0M8dUWk45hK1cx6SApyZp0sH59EpmZ8yJi0oEKrXCOPdm0CbKyrEkK994Lf/oTNG0allMr\npZTrhWUMG9bG70uMMRsBA3QBbrBzUhU8OtNSuUGXLpCXB8XFVsE2cyZMmQLXXgt6OSqllH11vpSK\nyAdAEnAbMAY4WUSWhDowVX8ej4e0tDTS0tLqVazpOAR77OSvoWvm2eFEl0HPnvDGG7BgATz5JJx+\nutXqVtEgrteePZo/ezR/9mj+nFXnu7sx5hagmYisFpHVQJwx5ubQh6ZUdCkuLiIjI438/H7k5/cj\nIyON4uLQ7Zvq5BiPvn3h3/+G7Gxri6vzz4dPP3UsHKWUinj1GcO2UkRSqt1WJCKODZLSMWwq0sTy\nmnmHDsH8+dYYt7PPtvYrPflkp6NSSqnwCcYYtvq8SzQyxvhPYoxpBOjOgko1QF1r5kWzxo3hxhth\n/Xro3dtav230aNi61enIlFIqctSnYHsHeMkYc4Ex5gLghfLbVITScQj2aP4C06wZ9O7tpaQEWre2\nxrvdey/s3Ol0ZJFDrz17NH/2aP6cVZ+CbRywGGu3gz8DHwD3hDIopaJNamoqJSXJVTZQj9U18+Lj\nrT1JV66EbdsgORlmzICff3Y6MqWUcq8G7SVqjEkAjiuffOAYHcOmIpGumVezNWuslraiIsjJgeHD\noVEjp6NSSqngCcYYtvpMOvACl2Kt2VYIfAd8JCJ32DmxHVqwqUjl8/l0zbxafPQRjBsHP/5obS5/\n8cXWHqZKKRXpwjXpoJWI7AYuBxaIyFnABXZOqpyl4xDssZO/hq6ZF22OlLs+fWDpUnjwQRg/Hvr1\ns4o49Sv927VH82eP5s9Z9XnHaGyM6QgMA94McTxKqRhmDFxyCaxaBf/3f3DNNTB0qNVtqpRSsaw+\nXaJXAvcBy0Tk5vK9RHNF5A/hCLCWmLRLVEUs7Ratv59/hr/+1ZqkcMkl1hi3445zOqrDeb3emNyM\nWil1uJpeD8LSJSoir4jIaSJyc/nxRieLNaUiWbh3O4h0Rx8Nd90FJSXQvj306vXrODc30a4ipVSF\nUL0e6Ed7G8K5L2Qw6ZuLPYHmz+fzkZs7ioyMlaSn7yM9fR8ZGSvJzR0VUdePHYHmrnVrmDbN2lx+\n505rKZCHH4b9+4Mbn9vp3649mj97NH/OauzUiY0xrYBngB6ADxgFlAAvAV2AUmCYiOxyKsYjqVii\nITnZWqJh1qxkMjPnxvwSDap2de12kJaW5lxwEeI3v4HZs639SSdOtAq37GwYOdLaUSGcvF6v/w0s\nJyfHf3v//v21e1SpGBOO14MGrcMWTMaYPOBDEZlnjGkMNAfuBbaLyMPGmHFAvIiMr+G+jo5hi+V9\nIWNJsMeaFRYWkp/fj/T0fVVuLyiIY/DgpVqwBeDTT60u0u++s1rgLrvMmaVAsrOzyc7ODv+JlVKu\nU9PrQcjHsBljTinfkuqYarcPtHNSY0xLoK+IzAMQkUPlLWmXAfPLf20+MNTOeUIllveFjBWhGGum\nux0E31lnwZIl1k4JWVlw7rlQUOB0VEopFXy1FmzGmNuARcAY4AtjzGWVfjzN5nm7Aj8YY+YZYz43\nxvzdGBMHtBeRbQAi8i3QzuZ5VA10HMKR1TXWLND8eTweMjPnkpeXQkFBHAUFceTl9SIzc67rWmVD\ndY2E4nGNgUGDrJ0Sbr4ZRoywZpR+8UXQT1WrcHWB6t+uPZo/ezR/9ROq14Mjjfq4CUgTkb3GmETg\nVWNMoojMAux2OjQGTgduEZEVxpjHgPFA9X7OWvs9MzIySExMBKB169akpKT4k1RxUYXqeNeuXSxd\n2pE+fTbg8Vh7IlZuKQn1+e0er1y50lXxuO346aefpkmTtf4W1PJ0+VtQ7eSvZ89UMjJmsH79es44\n4wxSU1NZunRplWngTj9/r9dLXl6eq+Kp7/H110O7dl5efx0uuKA/gwbBwIFeOnQI/fkruCkfeqzH\neuzMsdfrxev1UlpaSrDUOobNGPOliJxa6fgY4FVgDXC+iKQEfFJj2gMfi8gJ5cfpWAXbiUB/Edlm\njOkALBGRbjXc3/F12HRfyOilY82iY0zW7t3wyCPWOm4ZGdZ+pW3aOB2VUioWhXQvUWPMYuBOEVlZ\n6bbGwFzgOhGxtT2zMeZD4CYRKTHGZAFx5T/aISLT3TzpoIIugBqdYnVSScUnQrBmOWVlZQHWJ8eK\nT4+R6Ntv4f774ZVX4I474PbboXlzp6NSSsWSUBdsxwGHyseSVf/ZuSLyb1snNqYX1rIeTYCNwA1A\nI+BloDOwCWtZj5013NcVBVuk8lbqflM1O1ILaizkL1QtbE7mbv16mDQJli2DyZNh1Cho0sSRUAIW\nC9deKGn+7NH8BS4YBVutY9hE5H9H+JmtYq38MVYBZ9bwo9/afWyl7OrZM5W8vEJtQY0iSUnw0kuw\nYoW1FMijj1pLgVx+uTNLgSilVEM4tg6bHdrCplRoRfsnaRF47z0YP95qZZs+HaL46SqlHBbSLlE3\n04JNKRUMPh+8/PKvuyY89JC1X6lSSgVTWDZ/r3SylsaYhIovOydVzqoYWK4Co/kLnNty5/HA1VfD\n2rVw8cUwcCBcfz38979OR1Yzt+Uv0mj+7NH8OavOgs0YM9oY8y2wGigs/1oR6sCUUipcjjoKbr0V\nSkqssW5nnmnNJv3+e6cjU0opS51dosaY9cA5IvJDeEKqm3aJKqVC6bvv4IEH4PnnrcLtjjvgmGPq\nvp9SStUkXF2iG4F9df6WUkpFiXbt4C9/geXL4auvrFa3J5+EgwedjkzFCu1+VNXVp2CbAHxsjJlt\njPlLxVeoA1Ohoy8E9mj+AhdpuTvhBHjuOXj7bXj9dejWzVoaxOdzJp5Iy5/bRFL+3BirG2OKJfUp\n2GYDHwCf8OsYtsJQBqVil8/no7CwkMLCQnxOvSsqVU1qKrzzDvz979Z2V2eeCe+/73RUSqlYUp8x\nbEUi4qoNMnUMW3Sq2F0gOdnaXaCkJJnMzLm6P6tyFRF49VVrb9KuXa2lQE4/3emolNvVZ23DaN0e\nToVpHTZjzDSgFHgDOFBxu4jssHNiO7Rgiz6xun+nilwHD8KcOdY+peedZ01SOPFEp6NSbtXQ7d5C\ntT2ccka4Jh1cgzWO7SN0WY+o4MZxCEVFRSQnl1C5LvN4ICmpxL89lFu4MX+RIppy16QJ/OlP1h6l\nPXrAWWdZS4Ns2xa6c0ZT/pyg+bNH8+esWvcSrSAiXcMRiFJKRaLmza2dEkaPhqlToXt3q3C7+25o\n0cLp6JSTqndxVqhPF6d2garq6rU1lTGmB9AdOLriNhFZEMK46opHu0SjjHaJqmhRWgqTJ8O771rj\n3EaPhqZNnY5KOU27OGNbWLpEjTFZwOPlXwOAh4FL7ZxUqeo8Hg+ZmXPJy0uhoCCOgoI48vJ6kZk5\nV4s1FVESE2HBAqtg+9e/rKVAnn/euaVAlFLRoT7vhFcAFwDfisgNQC+gVUijUiHl1nEIPXumkpdX\nyODBSxk8eCl5eZ+7coaoW/MXCWIpd6edBm+9BfPmWYvwpqVZS4PY6RyIpfyFgpP5i4YuTr3+nFXn\nGDZgv4j4jDGHjDEtge+AziGOS8Uoj8dDWlqa02EoFTTnnQcffwwLF8LYsfCb38D06dZabip2REPB\nppxVn2U9ngTuBa4G7gL2AivLW9scoWPYlFKR6NAhq8UtJwfOOceapJCc7HRUSqlQC8s6bNVOmAi0\nFJHVdk5qlxZsSqlItm+f1U06Ywb84Q+QlQUdOzodlVIqVMI16eDGiu9FpBT4snwigopQOg7BHs1f\n4DR3lrg4GD8e1q2zlv7o0QMmTYJdu458P82fPZo/ezR/zqrPpIMLjDFvG2M6GmNOxdpTVFcXUkop\nmxISIDcXiopg61are/Sxx+DAgbrvq5SKLfVdh+0q4K/AT8C1IvLvUAdWRzzaJaqUijpffmmt3bZq\nlbXl1XXXQaNGTkellLIrXHuJJgHzgWKgG7AGuFNE9tk5sR1asCmlotmyZTBuHOzebW0uP3gwGFsv\n9UopJ4VrL9E3gPtEZDRwHrAe+MzOSZWzdByCPZq/wGnu6ic93Srapk6Fe+6B/v3hk080f3Zp/uzR\n/DmrPgVbbxH5AEAsM4DfhzYspZSKTRVvisbApZfC6tWQkQHDhsF998FXXzkanlLKIbUWbMaYewBE\nZLcx5spqP84IZVAqtHQBR3vclD+fz0dhYSGFhYX4ImDvIzflzq2qt2I0agQ33GDNKL3ssv707Qs3\n3QRbtjgTXyTT688ezZ+zjtTCdnWl7ydU+9nAEMSilKMirfgpLi4iIyON/Px+5Of3IyMjjeLiIqfD\nCqlI+z8KpmbN4O67oaQE2rSxtr4aPx5+/NHpyJRS4XCkgs3U8n1NxyqC6DiEwzWk+HFD/nw+H7m5\no8jIWEl6+j7S0/eRkbGS3NxRri5k7OQumgtUr9dLdnY22dnZ5OTk+L+vni+v10t8vDURYfVq2L7d\nWgokNxf273cm9kjihr/dSKb5c9aR9hKVWr6v6VipiFW5+PGUf4Tp08cqfvLyCvF46jPUM7yKiopI\nTi6hcmgeDyQllVBUVBR1+7FG4v9RQ/Tv379Kd1N2dnad9+nUCZ5+Gu68EyZOhMcft7a8GjFClwJR\nKhod6VWulzFmtzFmD3Ba+fcVxz3DFJ8KAR2HUFVdxU91mr/ABZq7hv4fRaua8tetG7z2Grz8MuTl\nWV2lixaBrnx0OP3btUfz56xaCzYRaSQiLUWkhYg0Lv++4rhJOINUSlWVmppKSUkylXs/fT5Yvz6Z\n1NRU5wJTtgX6pnj22eD1Wt2j993369IgSqnoENn9CCogOg6hqoYWP27In8fjITNzLnl5KRQUxFFQ\nENsM+xMAACAASURBVEdeXi8yM+e6unsw0NzFUoF6pIKtrvwZYy2yW1QEo0fD9ddbS4N8+WVwY4xU\nbvjbjWSaP2cdaQybUjGhovjJzR1FUlIJAOvXJ7m++OnZM5W8vEJ/l2Bqaqqr47UjUv+PnNKokTWW\nbdgweOopOP98q5DLyYHjj3c6OqVUIOq1l2hITmxMKbAL8AEHRaS3MSYeeAnoApQCw0RkVw331a2p\nVND5fL6YKH4iTeX/l169erFq1SpA/48aYtcuq6v0qadg1CiYMMHaeF4pFR5h2Us0VIwxG4E0Efmx\n0m3Tge0i8rAxZhwQLyLja7ivFmxKxYDi4iJyc0eRnGy1qpWUJJOZOZeePaOrGzRcvvnG2lT+1Vfh\nrrvgttsgLs7pqJSKfuHaSzRUTA3nvwxro3nK/x0a1ohihI5DsGfx4sUxu3irXQ259iJ1rblQsvu3\n27Gj1cr273/D559ba7g9/TQcOhSc+NxOX/vs0fw5y8mCTYD3jDGfGWP+r/y29iKyDUBEvgXa1XZn\nfbNUTiguLuKhh/4YlYu3uo0u5RE6ycnWMiCvvQYvvAA9eljfa8eFUu7lZJdoRxH5xhhzLPAucBuw\nSEQSKv3OdhFpU8N9ZcqUOO0eUWHl8/nIyEirsnirzwd5eSlRsXir2xQWFpKf34/09H1Vbi8oiGPw\n4KVRtziwU0Tg3Xdh3Dg4+miYPh3OO8/pqJSKLsHoEnVslqiIfFP+7/fGmIVAb2CbMaa9iGwzxnQA\nvqvt/suW7aN9+5Vcf/0gRo68h9NPP90/Hb6i2VaP9TiYxy1atCA5uYTVqwEgJcVq8WnceC1PP/00\no0ePdlW8kX7cr18/Zs1KJi7OKpBTUqwCuaCgI+ee++tcJLfEG6nHH37opWlT+Pzz/rz4Ilx9tZcu\nXeDvf+/Paac5H58e63EkHld8X1paSrA40sJmjIkDPCKy1xjTHKuFLQe4ANghItPrmnSwZIn1vX7a\nbjiv1+u/uFT9VbT4HHPMPlJSfr39ww+PZvDgpZx55pnOBRchGnrtVUw6qLqUx7yYbVUPx9/uL7/A\n7NkwdSpcdJE1SSExMaSnDBt97bNH8xe4SJ500B5YZowpAj4B3hCRd4HpwIXGmHVYxdtDDsWn1GFq\nW7z1o48O8Je/3KRj2UKgYq25wYOXMnjwUvLyPo/ZYi1cjjoKxoyB9evhhBMgLQ3uuAN++MHpyJSK\nbY6NYbOjooVNxw+pcLNafG6gS5fVNG4srFoFl1wCXbrotaii07ZtMGUKvPgijB1rFW/NmzsdlVKR\nJZJb2GyLlK14VHTp2TOVMWOe5ocfmtKhA9x6K3TtqrMXVfRq3x6eeAI++cTa4iopCf72Nzh40OnI\n3K/yeCal7IrYSke7RwKnLyL2fP7553Tq5OHkk0E/KzSMXnv2OJm/k06ylgB5801rCZBTT7WWBomk\nTppw5y/arvdoez6RJmLfbtLS0rRlTTkiKSkpZjYiV6q600+3lgF58kl4+GHo3RsWL3Y6KqWiX8SO\nYYvEuFX00NmLSlkfVF55BSZOhBNPhIceAjufWaJhFqLX6/W3ROXk5JCVlQVYyz5E+nNTgYvovUTt\n0IJNuYFuFq+U5eBBa4urKVNgwAB44AFrhmlDZWdnk52dHfT4nBJtz0cFLqYnHbiZz+dz9V6TOg7B\nnor8eTwe0tLSau2ed/t14AS99uxxa/6aNIGbb7aWAunWzeomve02+K7Wpc+d4db8RQrNn7Mc2+kg\nWlV0lSUnW11ls2bp9lmxSK8DVVmstMYecwzcdx/86U/WwrvdulmF2513QosWNd+nehdihWjoQoz0\n+JW7aJdoEOlekwr0OlBVVS/eY2kP5P/+FyZPhvfeg0mT4I9/tBbmrY12IapopV2iLlNUVERyckmV\npR50fa7Yo9eBquDz+cjNHUVGxkrS0/eRnr6PjIyV5OaOispu8updZl27wj/+Af/6F7z9ttXi9sIL\nEIVPXamQ04ItBuk4BHs0f4GLtdwFu3h3e/5qi69XL6tgmzMHZs6EM86wlgap3lES6i5Et+fP7TR/\nztKCLYhq22tS1+eKDRWTDHw+H+vWJel1oFQ1/ftbOyZMnGjtV3rhhbBiReWf93cqNKVcT8ewBZmu\nzxWbqo9TWr36OA4cgDPO+B+g10GsioXxjIGuO3bwIMybBzk5kJ5uLQWSlBSGgFXUiYT1+3QdNpeK\nlRlhylL7m3Ivxox5Go/Ho9dBDIulD3GBTBrYtw9mzYIZM2DYMGuSQocOoYlPRadImKyikw5cqq71\nuZym4xDsqZ6/2scprfdfC268DpwQi9dez56p5OUVMnjwUtt7IEdj/uLiYMIEWLcOmjWz9ii97z7Y\nvTv454rG/IVDRd40f87SddiUUirEKgr3aGenW6pNG6uV7bbbICvL6h69915rTbemTYMXo2o4N3Y5\nRvP6fbXRLlGlbIqFcUpKhVtxsVWwffEF3H8/XHstNGpk/3HdWHy4ndu7HN0eHwSnS1Rb2AKgY9RU\nZR6Ph8zMuTWMU5qr14ZSAerZE954AwoKYNw4eOQRa3P5gQPB2Hjb04KtfmKxBcvttIWtgaJh1XJ9\nwbKntvxpIV83vfbsidX8icCiRVaLW7t2MH06nHVWwx+noghxe2uM21S0YLn1+nNrXJXFdAubE2+O\nlVctrzhdnz7WquXa9aViZZySUuFmDAwdCkOGwPz5cMUV1gbz06bBySfXff+KQq20tJT58+f7b9fW\nougQK/+HEdvCNnx4SthbuQoLC8nP70d6+r4qtxcUxDF48FJ9s1ZKqTDYvx8efxxyc+Hyy61JCr/5\nTf3uGwnjndwmElqw3C6ml/UI5t58FSvUV6xSr5RSyr2aNYN77oGSEmjd2hrvdu+9sHOn05HVXyQt\nkaHFmjtEbMEWrL35iouLyMhIIz+/H/n5/cjISKO4uObHiZatpyLphcKNNH+B09zZo/mrKj7eGs+2\nahV89x0kJ1tLg/z8c82/76aWokj8v6wecyQ+h0gWsQVbMFQek1af1rqK2YB5eSkUFMRR8P/bu/cw\nq+p6j+Pv7+AFMAS0xAuk4mFEjcuIl8TbJF6CerA0VMx01Mzn2FFLM8C8dLwBYhr5pGUoQxYVYJ70\nJFFAA14eE3GQMYQhjSIP4gUcDBSV+Z4/fmt0wLns2Wtm1lp7f17PwzN7rdl7r59f18x891rf3/f3\neHcqK4doNqCIfEhX7Dtf374wbRpUVcETT4TErbIStm37+HPTkrAVAiVsnSuzNWwLFhC751W+NWma\nDSgiTSmEWeSF4KmnQiuQjRth4sQwWSFOK5AGcX/357vualqpHjB3RT1LtLJyaGI9rzQbUCSeQvzQ\no1nk6TF8OCxeDL//PYwfD7ffHm6dDh+e/3vumIxPndr2ZHzHxCyLyY76syUnwwnb0ti/8MvKypg6\ntZThw7fvUJ+1mrS2SlMdRxYpfvmrqqpizz17xv7Dl0bNrykb6mvb40Oezr3cmYUrayNHwi9+AWPH\nQr9+Vdx3XzmHHtq291IyHjScf1lPOrMqs2dZeyywrpo0kc7V1rpRkbi6dIELLgiLyw8eDOXlcPHF\nsHZt7u/RWjKeDyXe0lZFn5UMGlRGZeVSRo1azKhRi6msfC7zn/Rbo18U8Sh++evZs2e7/+FLi86Y\nRa5zL39du8I995RTWwt9+sDQoaE1yIYNyYwni/8vdxxzFv8bsqzoEzZon6t1IlLcivGKfRZnxPbq\nFVZIqKmBurqwUsLkyaEZb3MKpaVTe1PC1rkK87eItEhTseNR/PJXV1dX0H/4OvqKfZrOvbb0sEyL\nxvHbd1/46U9DG5AlS0IrkGnT4IMPPv66YkzGm5Km868YZXbSgYhkT8MfvilTLkpslnd7aW6mazHM\nIi+kIvyDD4Y5c+AvfwkzSn/wg9AK5PTTt28F0pCMF9rsZsmOzPZhy+K4RSTIeluPYu+3VqjrKrvD\nvHmhh9tuu8GkSXDCCUmPSgpBUfdhE5HsyvJVqEK6uiTbM4PPfx5OPRVmzgyzSw87LFxxGzQoPCfr\nHzYkuxI908ysxMyeM7NHou3eZvZHM1tlZvPMrGeS4ytUqkOIR/HLXyHEriNaPOQqLfHLahF+rvEr\nKYHzzoOVK+GUU8K/igqYN++FzNXttae0nH/FKumPBlcCKxptjwfmu/vBwEJgQiKjEhGRZhVLEf6u\nu8KVV0JtLfTr54we3Zd33jmPQYO6qoegdLrEatjMrC8wHbgVuMrdR5vZSuBEd19vZnsDVe4+sInX\nqoZNRBJRX19PRcWw7W6J5ruecdYV0+3BpUuXMmvWGFatupo///lsxoy5kzPPnMqzz5Lpuj3pHO1R\nw5bkT9ddwDVA48yrj7uvB3D3V4G9khiYiEhziuXqUi6KrYdljx7r+da3/ot77vksL788mPPPr2XJ\nkouabAUi0t4S+Qkzsy8A6919GdBSxqnLaB1AdQjxZD1+STY7zXrsGiS1QkqhxC8pceLXuG5vv/1e\n4oYbxnLzzaNZsuQ8zj//cObMCbNMC5nOv2QlNUv0WGC0mY0CugE9zOxB4FUz69Poluhrzb1BRUUF\nBxxwAAC9evVi6NChH3ZdbjiptN309rJly1I1nqxtZzl+NTXVXH31GPr1+xcHHtiFqVNLKS+/jP79\nB6RifFnbHjZsGFVVVSxevDgV49F2x25fc80DXH31GPr2DT8/q1dv49Zbl7Nhwzvcdls5U6bAOedU\nUVaWjvFqO7nthsdr1qyhvSTeh83MTgSujmrYbgfedPfJZjYO6O3u45t4jWrYRNpItVci8TVXt1df\nD7Nmwfe+F1ZNmDQJhgxJcqTZUQy1kFmvYWvKJOAUM1sFjIi2RaQdJNmOQqRQNFe3V1IC55wDL74I\nX/xi6Od23nnw978nONgMyOISZ0lJPGFz90XuPjp6vMHdT3b3g939VHd/K+nxFaLGl2yl7RS//Cl2\n8Sh+8XRG/HbZBb75zdAKpLQUjjwytAZ5/fUOP3SHa+/4NW5CfdxxW9QqpRWJJ2wi0jmy2uxUJIt6\n9IAbboAVUafRQw6Bm26Cf/872XGlSUdf9U9yglVHSLyGLR+qYRPJT8MamNsvvD69aNbAFEnKyy/D\n9dfDwoVw3XVwySXhalwx68g1adO23m971LApYRMpMsVQ4CuSVtXVMGEC/O1vcOutMGYMFOuPYEdN\nhErjBKtCnHQgnUB1MPFkPX5JNjvNeuySpvjFk4b4lZXBH/4A990Hd9wRatzmz096VLlp7/h1VBPq\nQp1glVQfNhERkaJ10knwzDMwZw5cdhnsv39oBVJsK1w1NKHWVf/W6ZaoiIhIgt5/H+6/P0xKOPFE\nuOUWOOigpEeVXYV6S1QJm4iISAps3gw//CHcdVfo6Xb99dCnT9Kjyqa0TbBSDZvkJQ11HFmm+OVP\nsYtH8Ysn7fHbbbewUsLKlWEG6aGHwo03wqZNSY8sSHv8Gktqvd+OpIRNREQkRT75SbjzTli6FNas\nCQ14f/Qj2Lo16ZFlS5ITrDqCbomKiIik2PLlcO21oQnvzTfD2LHF2wokq1TDJiIiUiQWL4Zx4+Cd\nd8KM0tNOA4uVAkhnUQ2b5CVLdQhplIX4pXVJlizELs0Uv3iyHr8TToCnngp1bd/6FowYEVqDdJas\nxy/rlLCJFJiammoqKoYxd+4JzJ17AhUVw6ipyW6zSBH5iBl8+cvwwgtw7rlwxhlhtYTa2qRHJh1N\nt0RFCkga+w+JSMfZsgXuvjusmnDmmeHq2z77JD0q2ZFuiYrIdgp1SRYRaVr37qGubdUq2H13+Mxn\nQmuQurqkRybtTQlbEVIdQjyKX/4Uu3gUv3gKOX577AG33w7LlsG6daEVyJ13wrvvtt8xCjl+WaCE\nTaSAlJWVUVtbSuN5BvX1sHp1KWVl2W4aKSKt69cPHngAFi6ERYtg4ED4+c9h27akRyZxqYZNpMCk\nbUkWEUnOk0+GW6Z1daEVyKhRagWSBPVhE5Em1dfXf1izVlZWpskGIkXMHR59FCZMgD33hMmT4Zhj\nkh5VcdGkA8mL6hDiyUL80rokSxZil2aKXzzFGj8zGD06rJhw4YVw9tmhHcjKlW17n2KNX1qk5ze5\niIiIdJguXULCtmoVDB8eGvFecgm88krSI5Nc6JaoiIhIEXrrrXB79L77QuI2bhz07p30qAqTbomK\niIhIXnr1gokTw63SDRtCK5ApU8JapZI+StiKkOoQ4lH88qfYxaP4xaP4NW2//cJVtscfh6efDonb\nAw/ABx9s/zzFL1lK2ERERISBA+Ghh2D2bJgxA4YMgd/9LswyleSphk1ERES24w5z58L48dCjR6h1\nO+64pEeVXerDJiIiIh1m2zaYOROuvx4GD4bbbgvrlUrbaNKB5EV1CPEofvlT7OJR/OJR/NquSxf4\n2tdCz7Z+/aoYMSK0BvnnP5MeWfFRwiYiIiIt6toVxoyB2lro2xfKyuA734E330x6ZMVDt0RFRESk\nTdatg5tugjlz4Kqr4MoroXv3pEeVXrolKiIiIp1un33g3nvD4vLV1aEVyM9+9vFWINJ+lLAVIdVx\nxKP45U+xiyet8auvr2fp0qUsXbqU+vr6pIfTrLTGLyuail9pKcyaBQ8/DL/6VZiQ8NvfqhVIR1DC\nJiIieaupqaaiYhhz557A3LknUFExjJqa6qSHJZ3syCNhwQKYOhVuvhmOOQYWLUp6VIUlkRo2M9sV\nWAzsEv37nbtfa2a9gd8A+wNrgLPcva6J16uGTUQkYfX19VRUDKOiYhklJQ37oLJyKJWVSykp0TWB\nYlRfD7/5DXzve6EZ78SJoQlvMctsDZu7bwU+5+5lwGDgJDM7FhgPzHf3g4GFwIQkxiciIq2rrq6m\ntLSWxnlZSQkMGFBLdbWushWrkhIYOza0Ahk5Ek47LbQGWbMm6ZFlW2Iff9x9S/Rw12gcG4HTgRnR\n/hnAlxIYWsFTHUc8il/+FLt4FL94FL942hq/XXaByy+H1avhoIPgiCPg29+GN97omPEVusQSNjMr\nMbNq4FWgyt1XAH3cfT2Au78K7JXU+EREpGVlZWXU1pbSeJ5BfT2sXl1KWVlZcgOTVOnRA77/ffjr\nX8Ms0oED4ZZbYPPmpEeWLYn3YTOz3YF5hNufv3X3PRp9701337OJ16iGTUQkBWpqqpky5SIGDKgF\nYPXqAVxzzXQGDVLCJk176aWw1FVVVfj69a/DzjsnPaqO1R41bDu112Dy5e6bzOwx4AhgvZn1cff1\nZrY38Fpzr6uoqOCAAw4AoFevXgwdOpTy8nLgo8u22ta2trW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      "text/plain": [
       "<matplotlib.figure.Figure at 0x114278e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the decision boundary: two points, draw a line between\n",
    "#Decision boundary occurs when h = 0, or when\n",
    "#theta0 + theta1*x1 + theta2*x2 = 0\n",
    "#y=mx+b is replaced by x2 = (-1/thetheta2)(theta0 + theta1*x1)\n",
    "\n",
    "boundary_xs = np.array([np.min(X[:,1]), np.max(X[:,1])])\n",
    "boundary_ys = (-1./theta[2])*(theta[0] + theta[1]*boundary_xs)\n",
    "plotData()\n",
    "plt.plot(boundary_xs,boundary_ys,'b-',label='Decision Boundary')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.776291590411\n"
     ]
    }
   ],
   "source": [
    "#For a student with an Exam 1 score of 45 and an Exam 2 score of 85, \n",
    "#you should expect to see an admission probability of 0.776.\n",
    "print h(theta,np.array([1, 45.,85.]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fraction of training samples correctly predicted: 0.890000.\n"
     ]
    }
   ],
   "source": [
    "def makePrediction(mytheta, myx):\n",
    "    return h(mytheta,myx) >= 0.5\n",
    "\n",
    "#Compute the percentage of samples I got correct:\n",
    "pos_correct = float(np.sum(makePrediction(theta,pos)))\n",
    "neg_correct = float(np.sum(np.invert(makePrediction(theta,neg))))\n",
    "tot = len(pos)+len(neg)\n",
    "prcnt_correct = float(pos_correct+neg_correct)/tot\n",
    "print \"Fraction of training samples correctly predicted: %f.\" % prcnt_correct "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2 Regularized Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1 Visualizing the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "datafile = 'data/ex2data2.txt'\n",
    "#!head $datafile\n",
    "cols = np.loadtxt(datafile,delimiter=',',usecols=(0,1,2),unpack=True) #Read in comma separated data\n",
    "##Form the usual \"X\" matrix and \"y\" vector\n",
    "X = np.transpose(np.array(cols[:-1]))\n",
    "y = np.transpose(np.array(cols[-1:]))\n",
    "m = y.size # number of training examples\n",
    "##Insert the usual column of 1's into the \"X\" matrix\n",
    "X = np.insert(X,0,1,axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Divide the sample into two: ones with positive classification, one with null classification\n",
    "pos = np.array([X[i] for i in xrange(X.shape[0]) if y[i] == 1])\n",
    "neg = np.array([X[i] for i in xrange(X.shape[0]) if y[i] == 0])\n",
    "#Check to make sure I included all entries\n",
    "#print \"Included everything? \",(len(pos)+len(neg) == X.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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4JsqesMeBXAfgjYrnb7ivURNx9ikPUt8d1d9EyfbyRYmx8DAWZvhJILO+1rsj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\nMIEQEVEg/x9OMNFmuRx+8wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x112ff8a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plotData():\n",
    "    plt.plot(pos[:,1],pos[:,2],'k+',label='y=1')\n",
    "    plt.plot(neg[:,1],neg[:,2],'yo',label='y=0')\n",
    "    plt.xlabel('Microchip Test 1')\n",
    "    plt.ylabel('Microchip Test 2')\n",
    "    plt.legend()\n",
    "    plt.grid(True)\n",
    "\n",
    "#Draw it square to emphasize circular features\n",
    "plt.figure(figsize=(6,6))\n",
    "plotData()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2 Feature mapping"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#This code I took from someone else (the OCTAVE equivalent was provided in the HW)\n",
    "def mapFeature( x1col, x2col ):\n",
    "    \"\"\" \n",
    "    Function that takes in a column of n- x1's, a column of n- x2s, and builds\n",
    "    a n- x 28-dim matrix of featuers as described in the homework assignment\n",
    "    \"\"\"\n",
    "    degrees = 6\n",
    "    out = np.ones( (x1col.shape[0], 1) )\n",
    "\n",
    "    for i in range(1, degrees+1):\n",
    "        for j in range(0, i+1):\n",
    "            term1 = x1col ** (i-j)\n",
    "            term2 = x2col ** (j)\n",
    "            term  = (term1 * term2).reshape( term1.shape[0], 1 ) \n",
    "            out   = np.hstack(( out, term ))\n",
    "    return out"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Create feature-mapped X matrix\n",
    "mappedX = mapFeature(X[:,1],X[:,2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.3 Cost function and gradient"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6931471805599453"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Cost function is the same as the one implemented above, as I included the regularization\n",
    "#toggled off for default function call (lambda = 0)\n",
    "#I do not need separate implementation of the derivative term of the cost function\n",
    "#Because the scipy optimization function I'm using only needs the cost function itself\n",
    "#Let's check that the cost function returns a cost of 0.693 with zeros for initial theta,\n",
    "#and regularized x values\n",
    "initial_theta = np.zeros((mappedX.shape[1],1))\n",
    "computeCost(initial_theta,mappedX,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.3.1 Learning parameters using fminunc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#I noticed that fmin wasn't converging (passing max # of iterations)\n",
    "#so let's use minimize instead\n",
    "\n",
    "def optimizeRegularizedTheta(mytheta,myX,myy,mylambda=0.):\n",
    "    result = optimize.minimize(computeCost, mytheta, args=(myX, myy, mylambda),  method='BFGS', options={\"maxiter\":500, \"disp\":False} )\n",
    "    return np.array([result.x]), result.fun\n",
    "    \n",
    "theta, mincost = optimizeRegularizedTheta(initial_theta,mappedX,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.4 Plotting the decision boundary"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plotBoundary(mytheta, myX, myy, mylambda=0.):\n",
    "    \"\"\"\n",
    "    Function to plot the decision boundary for arbitrary theta, X, y, lambda value\n",
    "    Inside of this function is feature mapping, and the minimization routine.\n",
    "    It works by making a grid of x1 (\"xvals\") and x2 (\"yvals\") points,\n",
    "    And for each, computing whether the hypothesis classifies that point as\n",
    "    True or False. Then, a contour is drawn with a built-in pyplot function.\n",
    "    \"\"\"\n",
    "    theta, mincost = optimizeRegularizedTheta(mytheta,myX,myy,mylambda)\n",
    "    xvals = np.linspace(-1,1.5,50)\n",
    "    yvals = np.linspace(-1,1.5,50)\n",
    "    zvals = np.zeros((len(xvals),len(yvals)))\n",
    "    for i in xrange(len(xvals)):\n",
    "        for j in xrange(len(yvals)):\n",
    "            myfeaturesij = mapFeature(np.array([xvals[i]]),np.array([yvals[j]]))\n",
    "            zvals[i][j] = np.dot(theta,myfeaturesij.T)\n",
    "    zvals = zvals.transpose()\n",
    "\n",
    "    u, v = np.meshgrid( xvals, yvals )\n",
    "    mycontour = plt.contour( xvals, yvals, zvals, [0])\n",
    "    #Kind of a hacky way to display a text on top of the decision boundary\n",
    "    myfmt = { 0:'Lambda = %d'%mylambda}\n",
    "    plt.clabel(mycontour, inline=1, fontsize=15, fmt=myfmt)\n",
    "    plt.title(\"Decision Boundary\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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JbG/GTRAE3+Dq1VxOncrg5MkMzp3LIj39KhcvXsv7a/r/8uVssrMNhR45OUZz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\nguBeimr2hAm1OXVqGAsXPm1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lZr611vNL2J4GPOqIwN/XsHWmiXPnshg9ehm7dp1my5b3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/CdTlYqUprZStlIMzv1JLzbiTFmObAnxGRVL0ZQSkXB38dwD9AamJrg4qgkpJmtlH00s1OTE458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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113a88b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Build a figure showing contours for various values of regularization parameter, lambda\n",
    "#It shows for lambda=0 we are overfitting, and for lambda=100 we are underfitting\n",
    "plt.figure(figsize=(12,10))\n",
    "plt.subplot(221)\n",
    "plotData()\n",
    "plotBoundary(theta,mappedX,y,0.)\n",
    "\n",
    "plt.subplot(222)\n",
    "plotData()\n",
    "plotBoundary(theta,mappedX,y,1.)\n",
    "\n",
    "plt.subplot(223)\n",
    "plotData()\n",
    "plotBoundary(theta,mappedX,y,10.)\n",
    "\n",
    "plt.subplot(224)\n",
    "plotData()\n",
    "plotBoundary(theta,mappedX,y,100.)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
